Degradation‐Shape‐Regularized Conditional Neural Processes for Cross‐Domain Bearing RUL Prediction With Uncertainty Quantification

Accurate remaining useful life (RUL) prediction is essential for the prognostics and health management of rolling bearings. However, distribution shifts across bearings and operating conditions, together with limited labeled degradation data, pose challenges to prediction accuracy and uncertainty quantification. To address these challenges, this paper proposes a degradation‐shape‐regularized conditional neural process (DSR‐CNP) framework for cross‐domain bearing RUL prediction. The framework learns a conditional predictive distribution through cross‐bearing tasks, using labeled bearing observations as context to predict RUL for unseen bearings without requiring their RUL labels or updating model parameters during inference. A temporal dependence encoder captures temporal dependencies within context windows to improve the representation of sensor–RUL relationships. Monotonicity and smoothness regularization are incorporated into the training objective to encourage RUL degradation predictions and suppress excessive temporal fluctuations. Experiments on the PHM2012 bearing dataset evaluate the framework under both cross‐bearing and cross‐condition settings. In the cross‐bearing experiments, the proposed method achieves an average RMSE of 0.038, MAE of 0.030, and of 0.98, outperforming the evaluated baselines in average point‐prediction accuracy. The nominal prediction intervals achieve an average PICP of 0.98 and MPIW of 0.22. Cross‐condition comparisons and ablation studies further support the contributions of temporal encoding and degradation shape regularization to predictive performance.